13L 2s
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Scale structure
Step pattern
LLLLLLLsLLLLLLs
sLLLLLLsLLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
8\15 to 7\13 (640.0¢ to 646.2¢)
Dark
6\13 to 7\15 (553.8¢ to 560.0¢)
TAMNAMS information
Descends from
2L 7s (balzano)
Ancestor's step ratio range
3:1 to 4:1 (parahard)
Related MOS scales
Parent
2L 11s
Sister
2L 13s
Daughters
15L 13s, 13L 15s
Neutralized
11L 4s
2-Flought
28L 2s, 13L 17s
Equal tunings
Equalized (L:s = 1:1)
8\15 (640.0¢)
Supersoft (L:s = 4:3)
31\58 (641.4¢)
Soft (L:s = 3:2)
23\43 (641.9¢)
Semisoft (L:s = 5:3)
38\71 (642.3¢)
Basic (L:s = 2:1)
15\28 (642.9¢)
Semihard (L:s = 5:2)
37\69 (643.5¢)
Hard (L:s = 3:1)
22\41 (643.9¢)
Superhard (L:s = 4:1)
29\54 (644.4¢)
Collapsed (L:s = 1:0)
7\13 (646.2¢)
| ↖ 12L 1s | ↑ 13L 1s | 14L 1s ↗ |
| ← 12L 2s | 13L 2s | 14L 2s → |
| ↙ 12L 3s | ↓ 13L 3s | 14L 3s ↘ |
┌╥╥╥╥╥╥╥┬╥╥╥╥╥╥┬┐ │║║║║║║║│║║║║║║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLsLLLLLLL
13L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 2 small steps, repeating every octave. 13L 2s is a great-grandchild scale of 2L 7s, expanding it by 6 tones. Generators that produce this scale range from 640¢ to 646.2¢, or from 553.8¢ to 560¢.
The dark generator for this scale corresponds to a superfourth (interval sharper than 4/3). This generator has almost no sensible interpretation except to be taken as 11/8, meaning the MOS is an 11+-limit scale.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 14|0 | 1 | LLLLLLLsLLLLLLs |
| 13|1 | 9 | LLLLLLsLLLLLLLs |
| 12|2 | 2 | LLLLLLsLLLLLLsL |
| 11|3 | 10 | LLLLLsLLLLLLLsL |
| 10|4 | 3 | LLLLLsLLLLLLsLL |
| 9|5 | 11 | LLLLsLLLLLLLsLL |
| 8|6 | 4 | LLLLsLLLLLLsLLL |
| 7|7 | 12 | LLLsLLLLLLLsLLL |
| 6|8 | 5 | LLLsLLLLLLsLLLL |
| 5|9 | 13 | LLsLLLLLLLsLLLL |
| 4|10 | 6 | LLsLLLLLLsLLLLL |
| 3|11 | 14 | LsLLLLLLLsLLLLL |
| 2|12 | 7 | LsLLLLLLsLLLLLL |
| 1|13 | 15 | sLLLLLLLsLLLLLL |
| 0|14 | 8 | sLLLLLLsLLLLLLL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Minor 1-mosstep | m1ms | s | 0.0¢ to 80.0¢ |
| Major 1-mosstep | M1ms | L | 80.0¢ to 92.3¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 92.3¢ to 160.0¢ |
| Major 2-mosstep | M2ms | 2L | 160.0¢ to 184.6¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 184.6¢ to 240.0¢ |
| Major 3-mosstep | M3ms | 3L | 240.0¢ to 276.9¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 276.9¢ to 320.0¢ |
| Major 4-mosstep | M4ms | 4L | 320.0¢ to 369.2¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 369.2¢ to 400.0¢ |
| Major 5-mosstep | M5ms | 5L | 400.0¢ to 461.5¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 461.5¢ to 480.0¢ |
| Major 6-mosstep | M6ms | 6L | 480.0¢ to 553.8¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 6L + s | 553.8¢ to 560.0¢ |
| Augmented 7-mosstep | A7ms | 7L | 560.0¢ to 646.2¢ | |
| 8-mosstep | Diminished 8-mosstep | d8ms | 6L + 2s | 553.8¢ to 640.0¢ |
| Perfect 8-mosstep | P8ms | 7L + s | 640.0¢ to 646.2¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 7L + 2s | 646.2¢ to 720.0¢ |
| Major 9-mosstep | M9ms | 8L + s | 720.0¢ to 738.5¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 8L + 2s | 738.5¢ to 800.0¢ |
| Major 10-mosstep | M10ms | 9L + s | 800.0¢ to 830.8¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 9L + 2s | 830.8¢ to 880.0¢ |
| Major 11-mosstep | M11ms | 10L + s | 880.0¢ to 923.1¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 10L + 2s | 923.1¢ to 960.0¢ |
| Major 12-mosstep | M12ms | 11L + s | 960.0¢ to 1015.4¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 11L + 2s | 1015.4¢ to 1040.0¢ |
| Major 13-mosstep | M13ms | 12L + s | 1040.0¢ to 1107.7¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 12L + 2s | 1107.7¢ to 1120.0¢ |
| Major 14-mosstep | M14ms | 13L + s | 1120.0¢ to 1200.0¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 13L + 2s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 8\15 | 640.000 | 560.000 | 1:1 | 1.000 | Equalized 13L 2s | |||||
| 47\88 | 640.909 | 559.091 | 6:5 | 1.200 | ||||||
| 39\73 | 641.096 | 558.904 | 5:4 | 1.250 | ||||||
| 70\131 | 641.221 | 558.779 | 9:7 | 1.286 | ||||||
| 31\58 | 641.379 | 558.621 | 4:3 | 1.333 | Supersoft 13L 2s | |||||
| 85\159 | 641.509 | 558.491 | 11:8 | 1.375 | ||||||
| 54\101 | 641.584 | 558.416 | 7:5 | 1.400 | ||||||
| 77\144 | 641.667 | 558.333 | 10:7 | 1.429 | ||||||
| 23\43 | 641.860 | 558.140 | 3:2 | 1.500 | Soft 13L 2s | |||||
| 84\157 | 642.038 | 557.962 | 11:7 | 1.571 | ||||||
| 61\114 | 642.105 | 557.895 | 8:5 | 1.600 | ||||||
| 99\185 | 642.162 | 557.838 | 13:8 | 1.625 | ||||||
| 38\71 | 642.254 | 557.746 | 5:3 | 1.667 | Semisoft 13L 2s | |||||
| 91\170 | 642.353 | 557.647 | 12:7 | 1.714 | ||||||
| 53\99 | 642.424 | 557.576 | 7:4 | 1.750 | ||||||
| 68\127 | 642.520 | 557.480 | 9:5 | 1.800 | ||||||
| 15\28 | 642.857 | 557.143 | 2:1 | 2.000 | Basic 13L 2s Scales with tunings softer than this are proper | |||||
| 67\125 | 643.200 | 556.800 | 9:4 | 2.250 | ||||||
| 52\97 | 643.299 | 556.701 | 7:3 | 2.333 | ||||||
| 89\166 | 643.373 | 556.627 | 12:5 | 2.400 | ||||||
| 37\69 | 643.478 | 556.522 | 5:2 | 2.500 | Semihard 13L 2s | |||||
| 96\179 | 643.575 | 556.425 | 13:5 | 2.600 | ||||||
| 59\110 | 643.636 | 556.364 | 8:3 | 2.667 | ||||||
| 81\151 | 643.709 | 556.291 | 11:4 | 2.750 | ||||||
| 22\41 | 643.902 | 556.098 | 3:1 | 3.000 | Hard 13L 2s | |||||
| 73\136 | 644.118 | 555.882 | 10:3 | 3.333 | ||||||
| 51\95 | 644.211 | 555.789 | 7:2 | 3.500 | ||||||
| 80\149 | 644.295 | 555.705 | 11:3 | 3.667 | ||||||
| 29\54 | 644.444 | 555.556 | 4:1 | 4.000 | Superhard 13L 2s | |||||
| 65\121 | 644.628 | 555.372 | 9:2 | 4.500 | ||||||
| 36\67 | 644.776 | 555.224 | 5:1 | 5.000 | ||||||
| 43\80 | 645.000 | 555.000 | 6:1 | 6.000 | ||||||
| 7\13 | 646.154 | 553.846 | 1:0 | → ∞ | Collapsed 13L 2s | |||||